Question

Let det M denotes the determinant of the matrix M. Let A and B be $3 \times 3$ matrices with det A = 3 and det B = 4. Then the det (2AB) is ________.

• A. 24
• B. 42
• C. 96
• D. 48

Hint:

$|kAB| = k^n |A||B|$. Don't forget to raise the scalar to the power of the matrix order!

Answer 1

The Correct Option is C

Step 1: Concept
Properties of determinants: $|kM| = k^n |M|$ (where $n$ is the order) and $|AB| = |A||B|$.
Step 2: Analysis
We need to find $\text{det}(2AB)$. - Order of matrices ($n$) = 3. - $|A| = 3$, $|B| = 4$.
Step 3: Calculation
$\text{det}(2AB) = 2^3 \times \text{det}(A) \times \text{det}(B)$ $= 8 \times 3 \times 4$ $= 8 \times 12 = 96$.
Step 4: Conclusion
The determinant is 96.
Final Answer:(C)